Nonlinear Dynamics Of Rotating Shallow Water Methods And Advances

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Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances

Author :
Publisher : Elsevier
ISBN 13 : 008048946X
Total Pages : 401 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances by :

Download or read book Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances written by and published by Elsevier. This book was released on 2007-04-03 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wave emission, the role of essentially nonlinear wave phenomena. The specificity of the book is that analytical, numerical, and experimental approaches are presented together and complement each other. Special attention is paid on explaining the methodology, e.g. multiple time-scale asymptotic expansions, averaging and removal of resonances, in what concerns theory, high-resolution finite-volume schemes, in what concerns numerical simulations, and turntable experiments with stratified fluids, in what concerns laboratory simulations. A general introduction into GFD is given at the beginning to introduce the problematics for non-specialists. At the same time, recent new results on nonlinear geostrophic adjustment, nonlinear waves, and equatorial dynamics, including some exact results on the existence of the slow manifold, wave breaking, and nonlinear wave solutions are presented for the first time in a systematic manner. · Incorporates analytical, numerical and experimental approaches in the geophysical fluid dynamics context· Combination of essentials in GFD, of the description of analytical, numerical and experimental methods (tutorial part), and new results obtained by these methods (original part)· Provides the link between GFD and mechanics (averaging method, the method of normal forms); GFD and nonlinear physics (shocks, solitons, modons, anomalous transport, periodic nonlinear waves)

Fronts, Waves and Vortices in Geophysical Flows

Author : Jan-Bert Flor
Publisher : Springer
ISBN 13 : 364211587X
Total Pages : 192 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Fronts, Waves and Vortices in Geophysical Flows by : Jan-Bert Flor

Download or read book Fronts, Waves and Vortices in Geophysical Flows written by Jan-Bert Flor and published by Springer. This book was released on 2010-06-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most well known structures in planetary atmospheres and the Earth’s oceans are jets or fronts interacting with vortices on a wide range of scales. The transition from one state to another, such as in unbalanced or adjustment flows, involves the generation of waves as well as the interaction of coherent structures with these waves. This book presents a fluid mechanics perspective to the dynamics of fronts and vortices and their interaction with waves in geophysical flows. It provides a basic physical background for modeling coherent structures in a geophysical context, and it gives essential information on advanced topics such as spontaneous wave emission and wavemomentum transfer in geophysical flows. Based on a set of lectures by leading specialists, this text is targeted at graduate students, researchers and engineers in geophysics and environmental fluid mechanics.

Geophysical Fluid Dynamics

Author : Vladimir Zeitlin
Publisher : Oxford University Press
ISBN 13 : 0198804334
Total Pages : 509 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Geophysical Fluid Dynamics by : Vladimir Zeitlin

Download or read book Geophysical Fluid Dynamics written by Vladimir Zeitlin and published by Oxford University Press. This book was released on 2018 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geophysical fluid dynamics examines the dynamics of stratified and turbulent motion of fluids in the ocean and outer core, and of gases in the atmosphere. This book explains key notions and fundamental processes of the dynamics of large- and medium-scale atmospheric and oceanic motions from the unifying viewpoint of the rotating shallow water model. The model plays a distinguished role in geophysical fluid dynamics. It has been used for about a century for conceptual understanding of various phenomena, for elaboration of approaches and methods to be used later in more complete models, for development and testing of numerical codes, and for many other purposes. In spite of its simplicity, the model grasps essential features of the complete "primitive equations" models, being their vertically averaged version, and gives an intuitive representation and clear vision of principal dynamical processes. This book is a combination of a course on geophysical fluid dynamics (Part 1), with explanations and illustrations of fundamentals, and problems, as well as a more advanced treatise of a range of principal dynamical phenomena (Part 2), including recently arisen approaches and applications (Part 3). Mathematics and physics underlying dynamical phenomena are explained, with necessary demonstrations. Yet, an important goal of the book is to develop the reader's physical intuition and qualitative insights.

Dispersive Shallow Water Waves

Author : Gayaz Khakimzyanov
Publisher : Springer Nature
ISBN 13 : 3030462676
Total Pages : 296 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Dispersive Shallow Water Waves by : Gayaz Khakimzyanov

Download or read book Dispersive Shallow Water Waves written by Gayaz Khakimzyanov and published by Springer Nature. This book was released on 2020-09-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves. Including both an overview of existing dispersive models, as well as recent breakthroughs, the authors maintain an ideal balance between theory and applications. From modelling tsunami waves to smaller scale coastal processes, this book will be an indispensable resource for those looking to be brought up-to-date in this active area of scientific research. Beginning with an introduction to various dispersive long wave models on the flat space, the authors establish a foundation on which readers can confidently approach more advanced mathematical models and numerical techniques. The first two chapters of the book cover modelling and numerical simulation over globally flat spaces, including adaptive moving grid methods along with the operator splitting approach, which was historically proposed at the Institute of Computational Technologies at Novosibirsk. Later chapters build on this to explore high-end mathematical modelling of the fluid flow over deformed and rotating spheres using the operator splitting approach. The appendices that follow further elaborate by providing valuable insight into long wave models based on the potential flow assumption, and modified intermediate weakly nonlinear weakly dispersive equations. Dispersive Shallow Water Waves will be a valuable resource for researchers studying theoretical or applied oceanography, nonlinear waves as well as those more broadly interested in free surface flow dynamics.

Vortex Structures in Fluid Dynamic Problems

Author : Hector Perez-De-Tejada
Publisher : BoD – Books on Demand
ISBN 13 : 9535129430
Total Pages : 282 pages
Book Rating : 4.5/5 (351 download)

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Book Synopsis Vortex Structures in Fluid Dynamic Problems by : Hector Perez-De-Tejada

Download or read book Vortex Structures in Fluid Dynamic Problems written by Hector Perez-De-Tejada and published by BoD – Books on Demand. This book was released on 2017-03-01 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents of the book cover topics on vortex dynamics in a variety of flow problems and describe observational measurements and their interpretation. The book contains 13 chapters that first include vortices in the earth and planetary sciences related to vortices in the Venus plasma wake and also on tropical cyclones and on rotating shallow water in the earth's atmosphere. Vortices in fluid problems include airplane wake vortices, vorticity evolution in free-shear flows, together with axisymmetric flows with swirl, as well as thermal conductivities in fluid layers. Vortices in relativistic fluids, in magnetic disks, solitons and vortices, and relaxation for point vortices were also examined. Other chapters describe conditions in a vortex bioreactor and in vortex yarn structures.

Waves in Flows

Author : Tomáš Bodnár
Publisher : Springer Nature
ISBN 13 : 3030678458
Total Pages : 362 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Waves in Flows by : Tomáš Bodnár

Download or read book Waves in Flows written by Tomáš Bodnár and published by Springer Nature. This book was released on 2021-04-29 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school “Waves in Flows”, held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include: Equatorial wave–current interactions Water–wave problems Gravity wave propagation Flow–acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.

Dynamics of the Equatorial Ocean

Author : John P. Boyd
Publisher : Springer
ISBN 13 : 3662554763
Total Pages : 517 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis Dynamics of the Equatorial Ocean by : John P. Boyd

Download or read book Dynamics of the Equatorial Ocean written by John P. Boyd and published by Springer. This book was released on 2017-09-25 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive introduction to the theory of equatorially-confined waves and currents in the ocean. Among the topics treated are inertial and shear instabilities, wave generation by coastal reflection, semiannual and annual cycles in the tropic sea, transient equatorial waves, vertically-propagating beams, equatorial Ekman layers, the Yoshida jet model, generation of coastal Kelvin waves from equatorial waves by reflection, Rossby solitary waves, and Kelvin frontogenesis. A series of appendices on midlatitude theories for waves, jets and wave reflections add further material to assist the reader in understanding the differences between the same phenomenon in the equatorial zone versus higher latitudes.

Handbook of Differential Equations: Evolutionary Equations

Author : C.M. Dafermos
Publisher : Elsevier
ISBN 13 : 9780080932590
Total Pages : 534 pages
Book Rating : 4.9/5 (325 download)

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Book Synopsis Handbook of Differential Equations: Evolutionary Equations by : C.M. Dafermos

Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2009-04-29 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: • A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications. • Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability • Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime • Geometric and diffractive optics, including wave interactions • Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity • Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable. - Review of new results in the area - Continuation of previous volumes in the handbook series covering evolutionary PDEs - New content coverage of DE applications

Handbook of Geomathematics

Author : Willi Freeden
Publisher : Springer Science & Business Media
ISBN 13 : 364201545X
Total Pages : 1371 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Handbook of Geomathematics by : Willi Freeden

Download or read book Handbook of Geomathematics written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2010-08-13 with total page 1371 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.

Transfer of Substance in Vortex and Wave Flows in One-Component and Multi-component Environment

Author : Tatiana Chaplina
Publisher : Springer Nature
ISBN 13 : 3031318560
Total Pages : 156 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Transfer of Substance in Vortex and Wave Flows in One-Component and Multi-component Environment by : Tatiana Chaplina

Download or read book Transfer of Substance in Vortex and Wave Flows in One-Component and Multi-component Environment written by Tatiana Chaplina and published by Springer Nature. This book was released on 2023-06-02 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of vortex and wave flows is one of the traditional problems of fluid mechanics, the practical importance of which has grown significantly in recent years. Consideration of the processes of substance transfer in such complex systems as natural water bodies is fraught with many difficulties of a methodological and fundamental nature: the extreme complexity of conducting a full-scale experiment, the complexity and variability of hydrophysical fields of the ocean and hydrometeorological conditions during research, and also, in some cases, the complexity and the variability of the properties of the transferred substance. In this connection, it is of particular interest to study the transfer of markers in stationary vortex and wave flows, which can form in laboratory facilities with constant external conditions. In this case, it is possible to avoid problems associated with the spatial and temporal variability of natural sources of vortex formations and directly trace the dependence of the characteristic flow parameters or the characteristics of the movement of solid or other objects placed during. This book presents the results of experimental and theoretical studies of the dynamics and structure of multiphase vortex flows and the nature of the transfer of three types of markers: solid-state (ice, plastic), immiscible with water (oil, oil, diesel) and soluble (aniline dyes, uranyl). The results will be important, first of all, for a better understanding of the behavior of various impurities in the circulation flows and more accurate prediction of their distribution in natural conditions (in a stratified hydrosphere and atmosphere).

IUTAM Symposium on Turbulence in the Atmosphere and Oceans

Author : David Dritschel
Publisher : Springer Science & Business Media
ISBN 13 : 9400703600
Total Pages : 298 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis IUTAM Symposium on Turbulence in the Atmosphere and Oceans by : David Dritschel

Download or read book IUTAM Symposium on Turbulence in the Atmosphere and Oceans written by David Dritschel and published by Springer Science & Business Media. This book was released on 2010-12-09 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text of the Persian poet Rum ̄ ̄ ?, written some eight centuries ago, and reproduced at the beginning of this book is still relevant to many of our pursuits of knowledge, not least of turbulence. The text illustrates the inability people have in seeing the whole thing, the ‘big picture’. Everybody looks into the problem from his/her vi- point, and that leads to disagreement and controversy. If we could see the whole thing, our understanding would become complete and there would be no cont- versy. The turbulent motion of the atmosphere and oceans, at the heart of the observed general circulation, is undoubtedly very complex and dif?cult to understand in its entirety. Even ‘bare’ turbulence, without rotation and strati?cation whose effects are paramount in the atmosphere and oceans, still poses great fundamental ch- lenges for understanding after a century of research. Rotating strati?ed turbulence is a relatively new research topic. It is also far richer, exhibiting a host of distinct wave types interacting in a complicated and often subtle way with long-lived - herent structures such as jets or currents and vortices. All of this is tied together by basic ?uid-dynamical nonlinearity, and this gives rise to a multitude of phen- ena: spontaneous wave emission, wave-induced transport, both direct and inverse energy scale cascades, lateral and vertical anisotropy, fronts and transport barriers, anomalous transport in coherent vortices, and a very wide range of dynamical and thermodynamical instabilities.

Physical and Mathematical Modeling of Earth and Environment Processes

Author : V. I. Karev
Publisher : Springer Nature
ISBN 13 : 3030995046
Total Pages : 332 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Physical and Mathematical Modeling of Earth and Environment Processes by : V. I. Karev

Download or read book Physical and Mathematical Modeling of Earth and Environment Processes written by V. I. Karev and published by Springer Nature. This book was released on 2022-05-11 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents short papers of participants of the 7th International Scientific Conference-School for Young Scientists "Physical and Mathematical Modeling of Earth and Environment Processes" (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences). The book includes theoretical and experimental studies of processes in the atmosphere, oceans, the lithosphere, and their interaction; environmental issues; problems of human impact on the environment; and methods of geophysical research.

Introduction to Turbulent Transfer of Particles, Temperature and Magnetic Fields

Author : Igor Rogachevskii
Publisher : Cambridge University Press
ISBN 13 : 1316518604
Total Pages : 271 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Introduction to Turbulent Transfer of Particles, Temperature and Magnetic Fields by : Igor Rogachevskii

Download or read book Introduction to Turbulent Transfer of Particles, Temperature and Magnetic Fields written by Igor Rogachevskii and published by Cambridge University Press. This book was released on 2021-08-05 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing key concepts in turbulent transport with an overview of analytical and statistical tools to advanced graduates and researchers.

Modeling Atmospheric and Oceanic Flows

Author : Thomas von Larcher
Publisher : John Wiley & Sons
ISBN 13 : 1118855922
Total Pages : 368 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis Modeling Atmospheric and Oceanic Flows by : Thomas von Larcher

Download or read book Modeling Atmospheric and Oceanic Flows written by Thomas von Larcher and published by John Wiley & Sons. This book was released on 2014-10-30 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling Atmospheric and Oceanic Flows: Insights from Laboratory Experiments and Numerical Simulations provides a broad overview of recent progress in using laboratory experiments and numerical simulations to model atmospheric and oceanic fluid motions. This volume not only surveys novel research topics in laboratory experimentation, but also highlights recent developments in the corresponding computational simulations. As computing power grows exponentially and better numerical codes are developed, the interplay between numerical simulations and laboratory experiments is gaining paramount importance within the scientific community. The lessons learnt from the laboratory–model comparisons in this volume will act as a source of inspiration for the next generation of experiments and simulations. Volume highlights include: Topics pertaining to atmospheric science, climate physics, physical oceanography, marine geology and geophysics Overview of the most advanced experimental and computational research in geophysics Recent developments in numerical simulations of atmospheric and oceanic fluid motion Unique comparative analysis of the experimental and numerical approaches to modeling fluid flow Modeling Atmospheric and Oceanic Flows will be a valuable resource for graduate students, researchers, and professionals in the fields of geophysics, atmospheric sciences, oceanography, climate science, hydrology, and experimental geosciences.

Shallow Water Waves on the Rotating Earth

Author : Nathan Paldor
Publisher : Springer
ISBN 13 : 3319202618
Total Pages : 77 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Shallow Water Waves on the Rotating Earth by : Nathan Paldor

Download or read book Shallow Water Waves on the Rotating Earth written by Nathan Paldor and published by Springer. This book was released on 2015-08-12 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes new theoretical advances concerning analytical solutions of the Rotating Shallow Water Equations, which will make it of great interest to graduate students and scientists in the fields of Geophysical Fluid Dynamics, Physical Oceanography, Dynamical Meteorology and Applied Mathematics. The new dispersion relations and meridional amplitude variations of waves derived in this book can be applied to observations in the atmosphere and ocean and also provide alternatives to the Spherical Harmonics basis of global-scale spectral numerical models.

Nonlinear Ocean Dynamics

Author : Maged Marghany
Publisher : Elsevier
ISBN 13 : 0128209259
Total Pages : 464 pages
Book Rating : 4.1/5 (282 download)

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Book Synopsis Nonlinear Ocean Dynamics by : Maged Marghany

Download or read book Nonlinear Ocean Dynamics written by Maged Marghany and published by Elsevier. This book was released on 2021-02-09 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Ocean Dynamics: Synthetic Aperture Radar delivers the critical tools needed to understand the latest technology surrounding the radar imaging of nonlinear waves, particularly microwave radar, as a main source to understand, analyze and apply concepts in the field of ocean dynamic surface. Filling the gap between modern physics quantum theory and applications of radar imaging of ocean dynamic surface, this reference is packed with technical details associated with the potentiality of synthetic aperture radar (SAR). The book also includes key methods needed to extract the value-added information necessary, such as wave spectra energy, current pattern velocity, internal waves, and more. This book also reveals novel speculation of a shallow coastal front: named as Quantized Marghany's Front. Rounding out with practical simulations of 4-D wave-current interaction patterns using using radar images, the book brings an effective new source of technology and applications for today’s coastal scientists and engineers. Solves specific problems surrounding the nonlinearity of ocean surface dynamics in synthetic aperture radar data Helps develop new algorithms for retrieving ocean wave spectra and ocean current movements from synthetic aperture radar Includes over 100 equations that illustrate how to follow examples in the book

A Nonlinear Progress to Modern Soliton Theory

Author : Colin Rogers
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1527591557
Total Pages : 166 pages
Book Rating : 4.5/5 (275 download)

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Book Synopsis A Nonlinear Progress to Modern Soliton Theory by : Colin Rogers

Download or read book A Nonlinear Progress to Modern Soliton Theory written by Colin Rogers and published by Cambridge Scholars Publishing. This book was released on 2022-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.